Hexrod Explained

By Wayne Cattanach

   Each of us has his or her own style of flyfishing. For some it might be a
broad range of situations, for others it may be tightly defined. There are
many factors that contribute to the ideal, some real, some imaginary. And
from this there also is a favorite rod that comes to mind to fish these
ideal waters. But as varied as the individuals so are the thoughts as to
what characteristics make the perfect rod. As a rod maker I've been lead
by my preferences in rod performance. The thought here is to report on
what I have seen and how it was done, a guideline of sorts not necessarily
for others to find the same results but as a basis for others to find and
work up rod designs they prefer.

A Fly Rod
        A simple definition of the function of a fly rod is that it is intended
to transmit energy applied to it to a fly line. The line in turn extends to
full length and comes to rest. Consequently, the fly rod needs to be made
with sufficient material to structurally withstand the forces needed to
allow the cast to occur without damage to the fly rod. And lastly, a fly rod
should preform its function with a character that is preferred by the

Mr. Garrison's Idea
     In search of a rod design method, Mr Garrison decided to use his
knowledge as an engineer. He set up a method of determining the
moments(forces) created by the various weights of the line, bamboo,
guides, and finish at locations through the length of a fly rod. To this he
applied the character of a f(b) stress curve which was a different way of
using that normal element of the material. Instead of using a fixed figure
he chose to vary the value to either increase or decrease the flexure of the
fly rod. His normal stress curve started with high values for the tip and
gradually diminished the values through the length of the rod. This gave
the greatest flexure to the tip and gradually stiffened the rod into the

A New Era
        Mr. Garrison developed his design ideas and mathematics in the late
20's and early 30's. During that era his only aids were paper and pencil and
slide rule. Today even the simplest calculators can do the mathematics.
Although, I'm told that one rod design still takes several evenings. That's
right, I've never done a manual run through of the math. Having been
computerized in the early 70's I saw Mr. Garrison's math as an ideal
application. But even with a computer involved an understanding of the
math is still needed.

Action Length
        Because the fly rod is gripped by the hand most feel that the actual
affect of the rod design ends at the cork grip. Consequently the action
length, that part of the rod that actually has character, is the distance
from the tip top to the top of the cork grip. Because the planing forms are
set in 5 " increments a figure for the action length that is divisible by 5 is
always chosen.

        A moment is defined as a force attempting to cause rotation about a
defined point. Where the direction of force and the arm of leverage are
perpendicular. As an example consider tightening  a nut with a wrench.
Let's use these given factors. From the center of the nut to the center of
the hand applying the force is 1' or 12". And the hand is applying a
pressure of 1 lb or 16 oz.
        Then the moments of this example would be as follows:

        L X P = M
        1' X 1# = 1 foot pound
        1' X 16oz = 16 foot ounces
        12" X 1# = 12 inch pounds
        12" X 16oz = 192 inch ounces

        All of the above are correct calculations and terms. However for our
purposes working with inch ounces will be the easiest. Inches to measure
distance (L) and ounces to measure weight (P).

Impact Factor
        Essentially this force is determined by the actual weight being hung
off the tip of the fly rod multiplied by a safety factor. The weight is that
of the fly line being fished and the weight of the tip top itself added
together and expressed in ounces. This figure is then multiplied by 4
which is the safety factor. Understand Mr. Garrison's mathematics deals
with static design.
Static means that the elements are at rest. In real life a fly rod is a
dynamic device it sees motion and other external forces other than that of
just the static weights. To visualize this consider the fly line laying on
the water surface. When the cast is started not only is the weight of the
fly line being lifted but also the surface drag applied by the water
contact. The 4 multiplier was derived at by tests that Mr. Garrison

An Example
        At present, a fly line is classified by the weight (in grains) of the
first 30' of the fly line. For a #4 weight fly line this is 120 grains. A
standard tip top weights about 8 grains. Because we will be working in
ounces these figures need to be converted into ounces. There are 437
grains per ounce. The tip impact factor would then be determined as

        Line =  120/347 = .275 oz
        Tip Top = 8/437 = .018 oz
                  Total = .293 oz
                 Factor     x4
           Tip Impact    1.172 oz

        It isn't often that you may wish to design a rod at 30',the distance
that all fly lines weights are standardized at, so another method is
needed. A simple and fairly accurate method would be to simply weigh the
entire fly line and then determine a weight per foot by dividing that total
weight by the total length of the fly line. This value would be weight/foot
which would then be multiplied by the line length desired.

Tip Moments
        Once the tip impact is determined then the moments that the tip
impact create can be calculated. For an action length let's imagine that we
are designing a 7' 6" (90") rod. Together the normal handle and reelseat are
10". So the action length of a 7' 6" rod is 80". And because the planing
forms are set at 5" increments the calculations of the tip impact would
look as follows:

        tip (1.172 x 0)  =  0.00
         5" (1.172 x 5   =  5.860
        10" (1.172 x 10) = 11.720
        80" (1.172 x 80) = 93.760

Line In Guides Moments
        To account for the line as it pass down the rod the center of gravity
for each location needs to be determined. The center of gravity could be
thought of as the balance point. An example would be if the point under
investigation is 5" location then the center of gravity would be 2.5"
because the line is of uniform weight. The line weight is calculated for
the appropriate line size. Looking back to our other line example, if 30' of
#4 weight line weighs 120 grains 1" weights .334 grains or .0008 oz. So
the moments for the line on the rod would look as follows:

        tip (.0008 x 0 x 0 x 4)   = .0000
         5" (.0008 x 5 x 2.5 x 4)  = .100
        10" (.0008 x 10 x 5 x 4)   = .160
        80 (.0008 x 80 x 40 x 4) = 10.240

Varnish And Guide Moments
        Because of their diminished effect on the final results Mr. Garrison
calculated these values one time and then used those figures as a standard
on all future rod designs. Even with the added power of a computer it
would be impractical to set up an alogarithm to come any closer that the
graphed values Mr. Garrison used.

Ferrule Moments
        The ferrule moments are calculated in the same fashion as the tip
moments except that there is no weight until the ferrules. In our example
if the 7'6"(90") rod is a 2 piece the ferrules are located at 45" so there
would be no ferrule moments until that point. From experience a 7' 6" 2
piece rod require a size 13/64 ferrule which weighs 118 grains or .271
ounce. Again a impact factor is used (multiply x 4) therefore the
calculations would be as follows:
        45" (.271 x 0 x 4)  = 0.000
        50" (.271 x 5 x 4)  = 1.355
        80" (.271 x 35 x 4) = 9.485

Center Of Gravity
        For those times that the ferrules aren't located on a 5" location then
the center of gravity of their weight needs to be accounted for. Unlike the
line that is off the rod the ferrules are a part of the rod and would use a
length figure from the actual location to the location under investigation.

Bamboo Moments
        These are the most complex to calculate and are of sufficient value
to make those calculation worthwhile. I'm not going into all the
mathematics of it all but just explain the concept. As you move from the
tip to the butt of the rod the dimensions across the flats increase or the
mass increases. Consequently a calculation to determine the center of
mass is required to determine the location of the leverage arm for
calculating the moments at each location.
        To start these values are of an imaginary rod. Then as the actual rod
dimensions are derived then these values are substituted to bring the
moments of the bamboo weight closer to their real life values.
Total Moments
        With all the individual moments calculated their values are added
together to reach total moments for each of the locations from the tip to
the end of action length. Remember that these totals are only temporary
that as new dimensions are generated then the moments are recalculated
because of the changes in the bamboo moments.

The Dimensions
        To determine the dimensions for the proposed rod design the total
moments and the allowable stress values are placed into the following

        Now as I have mentioned earlier these dimensions were only
temporary and to bring them into more accurate values the bamboo
moments are recalculated and then used with the allowable stress values
to get a second value and then a third refiguring occurred.
        A valid question that can be raised is whether more times through
the calculations would yield more accurate dimensions. Remember that in
real life we are only working to be physically accurate to the nearest
.001" and three derivations yield that mathematically.

In Real Life
        Well on paper the stress curve Mr. Garrison developed had a smooth
flow to it starting with a high value at the tip and gradually descending to
lower values in the butt section. However,  remember that the figured
dimensions for the tip weren't used by Mr. Garrison. He considered these
numbers to be unpractically small to make so he arbitrarily increased
them and then blended the new tip dimension into the natural slope of the
dimensional graph.
        But it is never mentioned in his writings what this did in real life to
his stress curve. Well, by adding material he consequently lowered the f(b)
values at the tip.
Between The Lines
        It is another of those unmentioned items that sets the mind to
wandering(wondering). But by simply rewriting the formula (I did it and I
flunked rocket science - so I find it hard to believe that Mr. G had at some
point in time) instead of solving for dimensions using stress values,
stress values can be derived from dimensions. In the text that leads up to
the explanation of the mathematics there is information that Mr. Garrison
may have used an 8' Payne in developing his stress curves.
        Whatever the case the program I ended up with is bidirectional as far
as stress values are concerned which can launch a person into discovering
the ideas of rodmakers other than Mr. Garrison. All that is needed are the
dimensions of a rod and to know at what distance that the castability of
the rod is maximized.
    I suspect that some where there is a note book that would tell all.

Program Accuracy
        It has been brought up that there are a few ever so slight differences
in the program I wrote, Hexrod, and the way Mr. Garrison did his math.
These differences are in the varnish and guide moments. To test to see
how agreeable the two are I ran a side by side comparison to see. The test
rod was the one that illustrates the math in his book. It might be pointed
out that some of the deviation might be from slide rule versus computer

                Mr.Garrison     Hexrod  delta
                        .047             047            -
                        .081            .081            -
                        .104            .104            -
                        .122            .122            -
                        .136            .137            .001
                        .150            .151            .001
                        .163            .164            .001
                        .175            .177            .003
                        .188            .189            .001
                        .199            .201            .002
                        .213            .214            .001
                        .227            .228            .001
                        .241            .242            .001
                        .254            .255            .001
                        .268            .269            .001
                        .282            .282            -
                        .296            .296            -

        As you can see the differences are small if any. But a better test
might be the program against itself. A second test would be given the
dimensions generated by the first run how close to the original stresses
will the program come?

                        Run #1          Run #2
                        196000          200838
                        196000          198957
                        189000          192663
                        184500          184546
                        180000          180010
                        175000          174825
                        170000          170980
                        167000          166210
                        164000          163895
                        161250          161417
                        158500          158655
                        156000          156115
                        153500          153333
                        151750          152362
                        150000          149668
                        148250          148819
                        146500          146605
        Then the most important test of all. For a third test I reentered the
stress values determined in the second run to see if I would get the same
dimensions as what were input for the second test. There were no
differences when carried out to the nearest thousands of an inch. Which
proved to me at least against itself Hexrod could yield repeated and
trustable results. I chose to forego any test which required digging out my
K & E log - log slide rule.

Revisited Garrison Curve
        As was mentioned earlier Mr. Garrison didn't adhere to the
dimensions that he obtained for his tip dimensions. Instead he chose to
alter the dimension upward to make it easier to make. Lets just for the
sake of seeing look at what his stress curve would look like if he had
plotted it with this tip alteration. Well the tip f(b) drops from the initial
196000 to just 51457.

        I have only made one rod based on the Garrison tapers. Here again a
personal preference. What I did was start miking rods and swapping tapers
with other makers. The swapping part is reminiscent of a earlier stage of
life involving baseball cards. With each newly obtained taper I would run
the numbers through Hexrod to see what the character of the rod looked
like stress curve wise. From this I narrowed down the different
characters of rod tapers to those that I liked. Can I describe the action?
Not really but I can show you the character graphically.

                Tip      45883
                05      145740
                10      171041
                15      169797
                20      171094
                25      153944
                30      150051
                35      129181
                40      133008
                45      151417
                50      150430
                55      144962
                60      145942
                65      153009
        A general description of the rod character would be that of a
parabolic. But I seldom use that term because of the immediate
association with what Mr. Garrison called a parabolic which tends to have
a cooling effect in some cane rod circles. But with a little imagination you
can see the distinct reversed 'J' of the curve which by most everyones
definition is a parabolic action. softer tip, rigid mid section, & a softer
butt. A reversed 'J' graph wise.

Action Speed
        Because a rod action is a bit difficult to define I will also include a
few graphs from other action rods just to perhaps add a little clarity. A
classic fast action dry fly action would look like this.

                Tip     103543
                05      283992
                10      255838
                15      268153
                20      191826
                25      189945
                30      164611
                35      181761
                40      177543
                45      177706
                50      163416
                55      151463
                60      113423
                65      108872
                70       99021
                75       91516

        The rod listed above is perhaps one of the real classics. A 1920's
Leonard Catskill 7'0" #2 weight.(Now how many quessed that one right
???) Here are a list of the numbers for those that would like them :

                Tip     .043
                 05     .053
                 10     .070
                 15     .080
                 20     .100
                 25     .110
                 30     .125
                 35     .130
                 40     .140
                 45     .150
                 50     .165
                 55     .180
                 60     .210
                 65     .225
                 70     .230
                 74     .230
                 75     .245
                 76     .265
                 80     .265
                 84     .265

        If you think about it for a minute it does make sense. A fast action
rod has a very soft tip descending into a very strong butt as you can see in
the numbers. Or as I refer to it a 'high amplitude' or f(b) range. And the
reverse is also true a rod with 'low amplitude' or f(b) range would have a
slow action.

Why Stresses Not Dimensions?
        I am often asked this question when discussing rod tapers and
alteration. As I pointed out earlier a f(b) curve only represents a character
and only relates to makable numbers when a tip impact factor, number of
sections, & such are applied. The character  remains the same whether it
is a 3 weight or a 4 weight, two piece or 3 piece. How ever if you were to
look at the dimensions of these rods there is little in common to be able
to alter with much success. Even if the compared rods are both the same
number of pieces but different line weights the general 'slope' of the
graphed dimensions will be different because of differing ferrule weights
and bamboo weights.
                                    6'3"            6'3"
                                  #3/2          #4/2

                Tip             .065            .070     .005 dif
                05              .077            .082
                10              .093            .100
                15              .108            .116
                20              .120            .128
                25              .137            .146
                30              .150            .160
                35              .169            .179
                40              .180            .191
                45              .185            .196
                50              .198            .209
                55              .213            .224
                60              .225            .236
                65              .233            .244     .011 dif

Things To Try
        Over the years some of what I think are the best casting rods were
blended characters. By this I actually curve averaged two distinct f(b)
curves from two rods creating a entirely new f(b) curve. The possibilities
could be viewed as endless b† are certainly limits to all workable
combinations. But rod design is not necessarily the myst that some make
it out to be. A good start might be to graph known tapers that you have
cast and know the feel of. Then perhaps you might design a 3 piece rod
with the same character as a 2 piece that you are familiar with. Then
move on to changing line sizes of rods that you have made. What you will
find is that instead of just concentrating on which fly to pick next time on
the stream you will start to think more about the character of the rod and
its part of the big picture.
The Next Step
        It may have been a presumption on my part but I advanced the cause
by simply rewriting Mr. Garrison's formula and started solving for f(b)
given dimensions. That way I could use his idea as a 'ruler' to investigate
other existing rods for their stress characteristics. To determine a tip
impact factor (weight of line hung off the rod tip) the rod under
investigation would be cast and the distance at which the rod maximized
was used as the value. This began to raise questions of how the energy
was supposed to 'flow' through a fly rod. Some of what I thought to be the
best casting rods had some of the most unusual stress curves.
        Beyond this, a stress curve only defines the character of a rod so by
recalculating different line weights, and number of sections different
rods were created with that same character.